Question

10) Two coherent sources emit waves that have a wavelength of 0.44 m. Determine whether constructive or destructive interference occurs at a point whose distances from the two sources are as follows: (a) 1.32 and 3.08m; (b) 2.67 and 3.33m; (c) 2.20 and 3.74m; (d) 1.10 and 4.18m.

The answers given are: 0.68 degrees, 1.4 degrees, 2.0 degrees

If you could explain as you go through the problem that would be fantastic thank you.

Answer 1

wavelength of two coherent source = 0.44 m

distances from the two sources are S1P and S2P then path difference is S2P - S1P

The path differece for constructive interference = n, where n = 1,2,3,4

i.e for constructive interference,

the path difference is integer multiples of incident wvelength (1, 2, 3, 4, 5 ....)

Similarly the

The path differece for destructive interference = (2n+1)/2, where n = 1,2,3,4

i.e for destructive interference,

the path difference is half odd integer multiples of incident wvelength (1/2, 3/2, 5/2 ....)

a) Now the path difference for 1.32 and 3.08 is S2P - S1P = 3.08 - 1.2 = 1.76 = 4 (0.44) = 4

So the interference is constructve interference

b) for the set of 2.67 m and 3.33 m, the path difference is S2P - S1P = 3.33 - 2.67 = 0.66 = 3(0.44)/2 = (3/2)

The path difference is odd half multiple integer(3/2), so the interference is desstructve interference

c) for the set of 2.20 and 3.74m, the path difference is S2P - S1P = 3.74 - 2.20 = 1.54 = 7(0.44)/2 = (7/2)

The path difference is odd half multiple integer (7/2), so the interference is destructve interference

d) for the set of 1.10 and 4.18m, the path difference is S2P - S1P = 4.18 - 1.10 = 3.08 = 7(0.44) = (7)

The path difference is multiple integer (7), so the interference is constructve interference